I don't send children home due to a virus (clear running noses and eyes) and it sounds like that's what has hold of this poor little guy. But I check for temperatures after a couple of hours in the morning and if the parents dosed a fever it will be coming back by then. If they have green mucous then it's probably bacterial and a fever will accompany that infection so that's a giveaway. But with a virus the temperature is usually a few degrees lower than normal.
In my opinion it's the fever that scares me and that's when children have to go home.